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A054563
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n*(n^2 - 1)*(n + 2)*(n^2 + 4*n + 6)/72.
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3
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0, 0, 6, 45, 190, 595, 1540, 3486, 7140, 13530, 24090, 40755, 66066, 103285, 156520, 230860, 332520, 468996, 649230, 883785, 1185030, 1567335, 2047276, 2643850, 3378700, 4276350, 5364450, 6674031, 8239770, 10100265, 12298320, 14881240
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Number of labeled pure 2-complexes on n nodes with 2 2-simplexes.
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REFERENCES
| L. Berzolari, Allgemeine Theorie der Ho"heren Ebenen Algebraischen Kurven, Encyclopa"die der Mathematischen Wissenschaften mit Einschluss ihrer Anwendungen. Band III_2. Heft 3, Leipzig: B.G. Teubner, 1906. p. 353.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
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FORMULA
| C(C(n, 3), 2) = 6*C(n, 4)+15*C(n, 5)+10*C(n, 6) = n*(n-1)*(n-2)*(n-3)*(n^2+2)/72.
a(2)=0, a(3)=0, a(4)=6, a(5)=45, a(6)=190, a(7)=595, a(8)=1540, a(n)=7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7) [From Harvey P. Dale, Sep 20 2011]
G.f.: -((x^2*(x*(x+3)+6))/(x-1)^7) [From Harvey P. Dale, Sep 20 2011]
a(n)=(binomial(n+2,3)^2-binomial(n+2,3))/2, n>0. [From Gary Detlefs, Nov 23 2011]
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MATHEMATICA
| Binomial[Binomial[Range[2, 40], 3], 2] (* or *) LinearRecurrence[ {7, -21, 35, -35, 21, -7, 1}, {0, 0, 6, 45, 190, 595, 1540}, 40] (* From Harvey P. Dale, Sep 20 2011 *)
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PROG
| (Other) sage: [(binomial(binomial(n, 3), 2)) for n in xrange(2, 34)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 30 2009]
(MAGMA) [n*(n^2 - 1)*(n + 2)*(n^2 + 4*n + 6)/72: n in [0..40]]; // Vincenzo Librandi, Sep 21 2011
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CROSSREFS
| Sequence in context: A204558 A123141 A122096 * A162230 A003486 A201191
Adjacent sequences: A054560 A054561 A054562 * A054564 A054565 A054566
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KEYWORD
| easy,nonn,nice
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 10 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 11 2000
Offset changed from 2 to 0 by Vincenzo Librandi, Sep 21 2011
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